Influences of substrate thickness on neutron specular reflection

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In specular reflection experiments the reflected beam from the end side of thick substrates is typically neglected. This is equivalent to assuming the substrates as semi-infinite matter. However, it is known that we should also consider the reflected beam from the end sides. Here we have investigated the effect of this consideration on the average reflectivity in a completely general case. It is shown that in some cases, especially in local minima of reflectivity vs. neutron wave number, this consideration can result in high enough differences such that it should be included in the interpretation of measured neutron specular reflectivity.